Problem: Solve for $x$ and $y$ using elimination. ${-6x-4y = -72}$ ${-5x+y = -21}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $4$ ${-6x-4y = -72}$ $-20x+4y = -84$ Add the top and bottom equations together. $-26x = -156$ $\dfrac{-26x}{{-26}} = \dfrac{-156}{{-26}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {-6x-4y = -72}\thinspace$ to find $y$ ${-6}{(6)}{ - 4y = -72}$ $-36-4y = -72$ $-36{+36} - 4y = -72{+36}$ $-4y = -36$ $\dfrac{-4y}{{-4}} = \dfrac{-36}{{-4}}$ ${y = 9}$ You can also plug ${x = 6}$ into $\thinspace {-5x+y = -21}\thinspace$ and get the same answer for $y$ : ${-5}{(6)}{ + y = -21}$ ${y = 9}$